Relative proportions of polycyclic aromatic hydrocarbons differ between accumulation bioassays and chemical methods to predict bioavailability

Chemical methods to predict the bioavailable fraction of organic contaminants are usually validated in the literature by comparison with established bioassays. A soil spiked with polycyclic aromatic hydrocarbons (PAHs) was aged over six months and subjected to butanol, cyclodextrin and tenax extractions as well as an exhaustive extraction to determine total PAH concentrations at several time points. Earthworm (Eisenia fetida) and rye grass root (Lolium multiflorum) accumulation bioassays were conducted in parallel. Butanol extractions gave the best relationship with earthworm accumulation (r2 ≤ 0.54, p ≤ 0.01); cyclodextrin, butanol and acetone–hexane extractions all gave good predictions of accumulation in rye grass roots (r2 ≤ 0.86, p ≤ 0.01). However, the profile of the PAHs extracted by the different chemical methods was significantly different (p < 0.01) to that accumulated in the organisms. Biota accumulated a higher proportion of the heavier 4-ringed PAHs. It is concluded that bioaccumulation is a complex process that cannot be predicted by measuring the bioavailable fraction alone. The ability of chemical methods to predict PAH accumulation in Eisenia fetida and Lolium multiflorum was hindered by the varied metabolic fate of the different PAHs within the organisms.

Scalability of efficient parallel K-Means

Clustering is defined as the grouping of similar items in a set, and is an important process within the field of data mining. As the amount of data for various applications continues to increase, in terms of its size and dimensionality, it is necessary to have efficient clustering methods. A popular clustering algorithm is K-Means, which adopts a greedy approach to produce a set of K-clusters with associated centres of mass, and uses a squared error distortion measure to determine convergence. Methods for improving the efficiency of K-Means have been largely explored in two main directions. The amount of computation can be significantly reduced by adopting a more efficient data structure, notably a multi-dimensional binary search tree (KD-Tree) to store either centroids or data points. A second direction is parallel processing, where data and computation loads are distributed over many processing nodes. However, little work has been done to provide a parallel formulation of the efficient sequential techniques based on KD-Trees. Such approaches are expected to have an irregular distribution of computation load and can suffer from load imbalance. This issue has so far limited the adoption of these efficient K-Means techniques in parallel computational environments. In this work, we provide a parallel formulation for the KD-Tree based K-Means algorithm and address its load balancing issues.

Dynamic load balancing in parallel KD-tree k-means

One among the most influential and popular data mining methods is the k-Means algorithm for cluster analysis. Techniques for improving the efficiency of k-Means have been largely explored in two main directions. The amount of computation can be significantly reduced by adopting geometrical constraints and an efficient data structure, notably a multidimensional binary search tree (KD-Tree). These techniques allow to reduce the number of distance computations the algorithm performs at each iteration. A second direction is parallel processing, where data and computation loads are distributed over many processing nodes. However, little work has been done to provide a parallel formulation of the efficient sequential techniques based on KD-Trees. Such approaches are expected to have an irregular distribution of computation load and can suffer from load imbalance. This issue has so far limited the adoption of these efficient k-Means variants in parallel computing environments. In this work, we provide a parallel formulation of the KD-Tree based k-Means algorithm for distributed memory systems and address its load balancing issue. Three solutions have been developed and tested. Two approaches are based on a static partitioning of the data set and a third solution incorporates a dynamic load balancing policy.

Amino acid pairing preferences in parallel beta-sheets in proteins

Statistical approaches have been applied to examine amino acid pairing preferences within parallel beta-sheets. The main chain hydrogen bonding pattern in parallel beta-sheets means that, for each residue pair, only one of the residues is involved in main chain hydrogen bonding with the strand containing the partner residue. We call this the hydrogen bonded (HB) residue and the partner residue the non-hydrogen bonded (nHB) residue, and differentiate between the favorability of a pair and that of its reverse pair, e.g. Asn(HB)-Thr(nHB)versus Thr(HB)-Asn(nHB). Significantly (p < or = 0.000001) favoured pairings were rationalised using stereochemical arguments. For instance, Asn(HB)-Thr(nHB) and Arg(HB)-Thr(nHB) were favoured pairs, where the residues adopted favoured chi1 rotamer positions that allowed side-chain interactions to occur. In contrast, Thr(HB)-Asn(nHB) and Thr(HB)-Arg(nHB) were not significantly favoured, and could only form side-chain interactions if the residues involved adopted less favourable chi1 conformations. The favourability of hydrophobic pairs e.g. Ile(HB)-Ile(nHB), Val(HB)-Val(nHB) and Leu(HB)-Ile(nHB) was explained by the residues adopting their most preferred chi1 and chi2 conformations, which enabled them to form nested arrangements. Cysteine-cysteine pairs are significantly favoured, although these do not form intrasheet disulphide bridges. Interactions between positively and negatively charged residues were asymmetrically preferred: those with the negatively charged residue at the HB position were more favoured. This trend was accounted for by the presence of general electrostatic interactions, which, based on analysis of distances between charged atoms, were likely to be stronger when the negatively charged residue is the HB partner. The Arg(HB)-Asp(nHB) interaction was an exception to this trend and its favorability was rationalised by the formation of specific side-chain interactions. This research provides rules that could be applied to protein structure prediction, comparative modelling and protein engineering and design. The methods used to analyse the pairing preferences are automated and detailed results are available (http://www.rubic.rdg.ac.uk/betapairprefsparallel/).

Amino acid pairing preferences in parallel beta-sheets in proteins

Statistical approaches have been applied to examine amino acid pairing preferences within parallel beta-sheets. The main chain hydrogen bonding pattern in parallel beta-sheets means that, for each residue pair, only one of the residues is involved in main chain hydrogen bonding with the strand containing the partner residue. We call this the hydrogen bonded (HB) residue and the partner residue the non-hydrogen bonded (nHB) residue, and differentiate between the favourability of a pair and that of its reverse pair, e.g. Asn(HB)-Thr(nHB) versus Thr(HB)-Asn(nHB). Significantly (p <= 0.000001) favoured pairings were rationalised using stereochemical arguments. For instance, Asn(HB)-Thr(nHB) and Arg(HB)-Thr(nHB) were favoured pairs, where the residues adopted favoured chi(1) rotamer positions that allowed side-chain interactions to occur. In contrast, Thr(HB)-Asn(nHB) and Thr(HB)-Arg(nHB) were not significantly favoured, and could only form side-chain interactions if the residues involved adopted less favourable chi(1) conformations. The favourability of hydrophobic pairs e.g. Ile(HB)-Ile(nHB), Val(HB)-Val(nHB) and Leu(HB)-Ile(nHB) was explained by the residues adopting their most preferred chi(1) and chi(2) conformations, which enabled them to form nested arrangements. Cysteine-cysteine pairs are significantly favoured, although these do not form intrasheet disulphide bridges. Interactions between positively and negatively charged residues were asymmetrically preferred: those with the negatively charged residue at the HB position were more favoured. This trend was accounted for by the presence of general electrostatic interactions, which, based on analysis of distances between charged atoms, were likely to be stronger when the negatively charged residue is the HB partner. The Arg(HB)-Asp(nHB) interaction was an exception to this trend and its favourability was rationalised by the formation of specific side-chain interactions. This research provides rules that could be applied to protein structure prediction, comparative modelling and protein engineering and design. The methods used to analyse the pairing preferences are automated and detailed results are available (http:// www.rubic.rdg.ac.uk/betapairprefsparallel/). (c) 2005 Elsevier Ltd. All rights reserved.

Parallel Monte Carlo approach for integration of the rendering equation

This paper is addressed to the numerical solving of the rendering equation in realistic image creation. The rendering equation is integral equation describing the light propagation in a scene accordingly to a given illumination model. The used illumination model determines the kernel of the equation under consideration. Nowadays, widely used are the Monte Carlo methods for solving the rendering equation in order to create photorealistic images. In this work we consider the Monte Carlo solving of the rendering equation in the context of the parallel sampling scheme for hemisphere. Our aim is to apply this sampling scheme to stratified Monte Carlo integration method for parallel solving of the rendering equation. The domain for integration of the rendering equation is a hemisphere. We divide the hemispherical domain into a number of equal sub-domains of orthogonal spherical triangles. This domain partitioning allows to solve the rendering equation in parallel. It is known that the Neumann series represent the solution of the integral equation as a infinity sum of integrals. We approximate this sum with a desired truncation error (systematic error) receiving the fixed number of iteration. Then the rendering equation is solved iteratively using Monte Carlo approach. At each iteration we solve multi-dimensional integrals using uniform hemisphere partitioning scheme. An estimate of the rate of convergence is obtained using the stratified Monte Carlo method. This domain partitioning allows easy parallel realization and leads to convergence improvement of the Monte Carlo method. The high performance and Grid computing of the corresponding Monte Carlo scheme are discussed.

Parallel Monte Carlo sampling scheme for sphere and hemisphere

The sampling of certain solid angle is a fundamental operation in realistic image synthesis, where the rendering equation describing the light propagation in closed domains is solved. Monte Carlo methods for solving the rendering equation use sampling of the solid angle subtended by unit hemisphere or unit sphere in order to perform the numerical integration of the rendering equation. In this work we consider the problem for generation of uniformly distributed random samples over hemisphere and sphere. Our aim is to construct and study the parallel sampling scheme for hemisphere and sphere. First we apply the symmetry property for partitioning of hemisphere and sphere. The domain of solid angle subtended by a hemisphere is divided into a number of equal sub-domains. Each sub-domain represents solid angle subtended by orthogonal spherical triangle with fixed vertices and computable parameters. Then we introduce two new algorithms for sampling of orthogonal spherical triangles. Both algorithms are based on a transformation of the unit square. Similarly to the Arvo's algorithm for sampling of arbitrary spherical triangle the suggested algorithms accommodate the stratified sampling. We derive the necessary transformations for the algorithms. The first sampling algorithm generates a sample by mapping of the unit square onto orthogonal spherical triangle. The second algorithm directly compute the unit radius vector of a sampling point inside to the orthogonal spherical triangle. The sampling of total hemisphere and sphere is performed in parallel for all sub-domains simultaneously by using the symmetry property of partitioning. The applicability of the corresponding parallel sampling scheme for Monte Carlo and Quasi-D/lonte Carlo solving of rendering equation is discussed.

Parallel Hybrid Monte Carlo Algorithms for Matrix Computations

In this paper we consider hybrid (fast stochastic approximation and deterministic refinement) algorithms for Matrix Inversion (MI) and Solving Systems of Linear Equations (SLAE). Monte Carlo methods are used for the stochastic approximation, since it is known that they are very efficient in finding a quick rough approximation of the element or a row of the inverse matrix or finding a component of the solution vector. We show how the stochastic approximation of the MI can be combined with a deterministic refinement procedure to obtain MI with the required precision and further solve the SLAE using MI. We employ a splitting A = D – C of a given non-singular matrix A, where D is a diagonal dominant matrix and matrix C is a diagonal matrix. In our algorithm for solving SLAE and MI different choices of D can be considered in order to control the norm of matrix T = D –1C, of the resulting SLAE and to minimize the number of the Markov Chains required to reach given precision. Further we run the algorithms on a mini-Grid and investigate their efficiency depending on the granularity. Corresponding experimental results are presented.

Parallel Monte Carlo algorithms for information retrieval

In any data mining applications, automated text and text and image retrieval of information is needed. This becomes essential with the growth of the Internet and digital libraries. Our approach is based on the latent semantic indexing (LSI) and the corresponding term-by-document matrix suggested by Berry and his co-authors. Instead of using deterministic methods to find the required number of first "k" singular triplets, we propose a stochastic approach. First, we use Monte Carlo method to sample and to build much smaller size term-by-document matrix (e.g. we build k x k matrix) from where we then find the first "k" triplets using standard deterministic methods. Second, we investigate how we can reduce the problem to finding the "k"-largest eigenvalues using parallel Monte Carlo methods. We apply these methods to the initial matrix and also to the reduced one. The algorithms are running on a cluster of workstations under MPI and results of the experiments arising in textual retrieval of Web documents as well as comparison of the stochastic methods proposed are presented. (C) 2003 IMACS. Published by Elsevier Science B.V. All rights reserved.

Monte Carlo methods for matrix computations on the grid

Many scientific and engineering applications involve inverting large matrices or solving systems of linear algebraic equations. Solving these problems with proven algorithms for direct methods can take very long to compute, as they depend on the size of the matrix. The computational complexity of the stochastic Monte Carlo methods depends only on the number of chains and the length of those chains. The computing power needed by inherently parallel Monte Carlo methods can be satisfied very efficiently by distributed computing technologies such as Grid computing. In this paper we show how a load balanced Monte Carlo method for computing the inverse of a dense matrix can be constructed, show how the method can be implemented on the Grid, and demonstrate how efficiently the method scales on multiple processors. (C) 2007 Elsevier B.V. All rights reserved.

Computational complexity of weighted splitting schemes on parallel computers

In models of complicated physical-chemical processes operator splitting is very often applied in order to achieve sufficient accuracy as well as efficiency of the numerical solution. The recently rediscovered weighted splitting schemes have the great advantage of being parallelizable on operator level, which allows us to reduce the computational time if parallel computers are used. In this paper, the computational times needed for the weighted splitting methods are studied in comparison with the sequential (S) splitting and the Marchuk-Strang (MSt) splitting and are illustrated by numerical experiments performed by use of simplified versions of the Danish Eulerian model (DEM).

Robust nonlinear model identification methods using forward regression

In this correspondence new robust nonlinear model construction algorithms for a large class of linear-in-the-parameters models are introduced to enhance model robustness via combined parameter regularization and new robust structural selective criteria. In parallel to parameter regularization, we use two classes of robust model selection criteria based on either experimental design criteria that optimizes model adequacy, or the predicted residual sums of squares (PRESS) statistic that optimizes model generalization capability, respectively. Three robust identification algorithms are introduced, i.e., combined A- and D-optimality with regularized orthogonal least squares algorithm, respectively; and combined PRESS statistic with regularized orthogonal least squares algorithm. A common characteristic of these algorithms is that the inherent computation efficiency associated with the orthogonalization scheme in orthogonal least squares or regularized orthogonal least squares has been extended such that the new algorithms are computationally efficient. Numerical examples are included to demonstrate effectiveness of the algorithms.

Neurofuzzy mixture of experts network parallel learning and model construction algorithms

A connection between a fuzzy neural network model with the mixture of experts network (MEN) modelling approach is established. Based on this linkage, two new neuro-fuzzy MEN construction algorithms are proposed to overcome the curse of dimensionality that is inherent in the majority of associative memory networks and/or other rule based systems. The first construction algorithm employs a function selection manager module in an MEN system. The second construction algorithm is based on a new parallel learning algorithm in which each model rule is trained independently, for which the parameter convergence property of the new learning method is established. As with the first approach, an expert selection criterion is utilised in this algorithm. These two construction methods are equivalent in their effectiveness in overcoming the curse of dimensionality by reducing the dimensionality of the regression vector, but the latter has the additional computational advantage of parallel processing. The proposed algorithms are analysed for effectiveness followed by numerical examples to illustrate their efficacy for some difficult data based modelling problems.

Two methods for modelling the propagation of terahertz radiation in a layered structure

Modelling the interaction of terahertz(THz) radiation with biological tissueposes many interesting problems. THzradiation is neither obviously described byan electric field distribution or anensemble of photons and biological tissueis an inhomogeneous medium with anelectronic permittivity that is bothspatially and frequency dependent making ita complex system to model.A three-layer system of parallel-sidedslabs has been used as the system throughwhich the passage of THz radiation has beensimulated. Two modelling approaches havebeen developed a thin film matrix model anda Monte Carlo model. The source data foreach of these methods, taken at the sametime as the data recorded to experimentallyverify them, was a THz spectrum that hadpassed though air only.Experimental verification of these twomodels was carried out using athree-layered in vitro phantom. Simulatedtransmission spectrum data was compared toexperimental transmission spectrum datafirst to determine and then to compare theaccuracy of the two methods. Goodagreement was found, with typical resultshaving a correlation coefficient of 0.90for the thin film matrix model and 0.78 forthe Monte Carlo model over the full THzspectrum. Further work is underway toimprove the models above 1 THz.